Rigid cohomology:
Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the se...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2007
|
| Series: | Cambridge tracts in mathematics
172 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Summary: | Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas. |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xv, 319 Seiten 23 cm |
| ISBN: | 9780521875240 0521875242 |
Staff View
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| 520 | 3 | |a Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas. | |
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Record in the Search Index
| _version_ | 1804137635447308288 |
|---|---|
| adam_text | Contents
Preface
page
ix
1
1
2
З
4
5
6
7
1
Introduction
1.1
Alice and Bob
1.2
Complexity
1.3
Weil conjectures
1.4
Zeta
functions
1.5
Arithmetic cohomology
1.6
Bloch-Ogus cohomology
1.7
Frobenius on rigid cohomology
1.8
Slopes of Frobenius
1.9
The coefficients question
1.10
F-isocrystals
2
Tubes
2.1
Some rigid geometry
2.2
Tubes of radius one
2.3
Tubes of smaller radius
3
Strict neighborhoods
3.1
Frames
3.2
Frames and tubes
3.3
Strict neighborhoods and tubes
3.4
Standard neighborhoods
4
Calculus
4.1
Calculus in rigid analytic geometry
4.2
Examples
12
12
16
23
35
35
43
54
65
74
74
83
VH
viii Contents
4.3
Calculus on strict neighborhoods
97
4.4
Radius of convergence
107
5
Overconvergent sheaves
125
5.1
Overconvergent sections
125
5.2
Overconvergence and abelian sheaves
137
5.3
Dagger modules
153
5.4
Coherent dagger modules
160
6
Overconvergent calculus
177
6.1
Stratifications and overconvergence
177
6.2
Cohomology
184
6.3
Cohomology with support in a closed subset
192
6.4
Cohomology with compact support
198
6.5
Comparison theorems
211
7
Overconvergent isocrystals
230
7.1
Overconvergent isocrystals on a frame
230
7.2
Overconvergence and calculus
236
7.3
Virtual frames
245
7.4
Cohomology of virtual frames
251
8
Rigid cohomology
264
8.1
Overconvergent isocrystal on an algebraic variety
264
8.2
Cohomology
271
8.3
Frobenius action
286
299
299
300
302
303
304
306
307
310
315
9
Conclusion
9.1
A brief history
9.2
Crystalline cohomology
9.3
Alterations and applications
9.4
The Crew conjecture
9.5
Kedlaya s methods
9.6
Arithmetic
ľ-modules
9.7
Log poles
References
Index
|
| adam_txt |
Contents
Preface
page
ix
1
1
2
З
4
5
6
7
1
Introduction
1.1
Alice and Bob
1.2
Complexity
1.3
Weil conjectures
1.4
Zeta
functions
1.5
Arithmetic cohomology
1.6
Bloch-Ogus cohomology
1.7
Frobenius on rigid cohomology
1.8
Slopes of Frobenius
1.9
The coefficients question
1.10
F-isocrystals
2
Tubes
2.1
Some rigid geometry
2.2
Tubes of radius one
2.3
Tubes of smaller radius
3
Strict neighborhoods
3.1
Frames
3.2
Frames and tubes
3.3
Strict neighborhoods and tubes
3.4
Standard neighborhoods
4
Calculus
4.1
Calculus in rigid analytic geometry
4.2
Examples
12
12
16
23
35
35
43
54
65
74
74
83
VH
viii Contents
4.3
Calculus on strict neighborhoods
97
4.4
Radius of convergence
107
5
Overconvergent sheaves
125
5.1
Overconvergent sections
125
5.2
Overconvergence and abelian sheaves
137
5.3
Dagger modules
153
5.4
Coherent dagger modules
160
6
Overconvergent calculus
177
6.1
Stratifications and overconvergence
177
6.2
Cohomology
184
6.3
Cohomology with support in a closed subset
192
6.4
Cohomology with compact support
198
6.5
Comparison theorems
211
7
Overconvergent isocrystals
230
7.1
Overconvergent isocrystals on a frame
230
7.2
Overconvergence and calculus
236
7.3
Virtual frames
245
7.4
Cohomology of virtual frames
251
8
Rigid cohomology
264
8.1
Overconvergent isocrystal on an algebraic variety
264
8.2
Cohomology
271
8.3
Frobenius action
286
299
299
300
302
303
304
306
307
310
315
9
Conclusion
9.1
A brief history
9.2
Crystalline cohomology
9.3
Alterations and applications
9.4
The Crew conjecture
9.5
Kedlaya's methods
9.6
Arithmetic
ľ-modules
9.7
Log poles
References
Index |
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| author | Le Stum, Bernard 1959- |
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| callnumber-label | QA612 |
| callnumber-raw | QA612.3 |
| callnumber-search | QA612.3 |
| callnumber-sort | QA 3612.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 320 |
| classification_tum | MAT 144f MAT 143f |
| ctrlnum | (OCoLC)132298497 (DE-599)BVBBV023304835 |
| dewey-full | 514.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.23 |
| dewey-search | 514.23 |
| dewey-sort | 3514.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:48:03Z |
| indexdate | 2024-07-09T21:15:26Z |
| institution | BVB |
| isbn | 9780521875240 0521875242 |
| language | English |
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| physical | xv, 319 Seiten 23 cm |
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| spelling | Le Stum, Bernard 1959- Verfasser (DE-588)1023217325 aut Rigid cohomology Bernard Le Stum (Université de Rennes I, France) Cambridge Cambridge University Press 2007 xv, 319 Seiten 23 cm txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 172 Includes bibliographical references and index Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas. Homologie Homology theory Kristalline Kohomologie (DE-588)4494390-8 gnd rswk-swf Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Kristalline Kohomologie (DE-588)4494390-8 s Verallgemeinerung (DE-588)4316262-9 s DE-604 Cambridge tracts in mathematics 172 (DE-604)BV000000001 172 http://www.loc.gov/catdir/enhancements/fy0808/2008530054-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0808/2008530054-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0808/2008530054-t.html Table of contents only Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Le Stum, Bernard 1959- Rigid cohomology Cambridge tracts in mathematics Homologie Homology theory Kristalline Kohomologie (DE-588)4494390-8 gnd Verallgemeinerung (DE-588)4316262-9 gnd |
| subject_GND | (DE-588)4494390-8 (DE-588)4316262-9 |
| title | Rigid cohomology |
| title_auth | Rigid cohomology |
| title_exact_search | Rigid cohomology |
| title_exact_search_txtP | Rigid cohomology |
| title_full | Rigid cohomology Bernard Le Stum (Université de Rennes I, France) |
| title_fullStr | Rigid cohomology Bernard Le Stum (Université de Rennes I, France) |
| title_full_unstemmed | Rigid cohomology Bernard Le Stum (Université de Rennes I, France) |
| title_short | Rigid cohomology |
| title_sort | rigid cohomology |
| topic | Homologie Homology theory Kristalline Kohomologie (DE-588)4494390-8 gnd Verallgemeinerung (DE-588)4316262-9 gnd |
| topic_facet | Homologie Homology theory Kristalline Kohomologie Verallgemeinerung |
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